How do I know which ones can be simplified? For instance, the next composite function g o f:

appears to work:

well, that's just multiplying the "2" in but, yes, it is a little "simplified".

Then I believe the domain would be {x|x not= 0}.[/QUOTE]
No. You cannot divide by 0 but here, the denominator is 1+ x. That is 0 when x= -1, not when x=0. If x= 0, that would be sin(0)= 0 which is well defined.

I think I'm starting to understand how these work. I was expecting them to work like identities and have multiple steps to get to the point where I can determine the domain, but it appears that isn't the true.